Collective in-plane magnetization in a 2D XY macrospin system within the framework of generalized Ott-Antonsen theory
arXiv:1912.02575 · doi:10.1098/rsta.2019.0259
Abstract
The problem of magnetic transitions between the low-temperature (macrospin ordered) phases in 2D XY arrays is addressed. The system is modeled as a plane structure of identical single-domain particles arranged in a square lattice and coupled by the magnetic dipole-dipole interaction; all the particles possess a strong easy-plane magnetic anisotropy. The basic state of the system in the considered temperature range is an antiferromagnetic (AF) stripe structure, where the macrospins (particle magnetic moments) are still involved in thermofluctuational motion: the superparamagnetic blocking temperature is lower than that () of the AF transition. The description is based on the stochastic equations governing the dynamics of individual magnetic moments, where the interparticle interaction is added in the mean field approximation. With the technique of a generalized Ott-Antonsen theory, the dynamics equations for the order parameters (including the macroscopic magnetization and the antiferromagnetic order parameter) and the partition function of the system are rigorously obtained and analysed. We show that inside the temperature interval of existence of the AF phase, a static external field tilted to the plane of the array is able to induce first order phase transitions from AF to ferromagnetic state; the phase diagrams displaying stable and metastable regions of the system are presented.
arXiv comment18 pages, 3 figures
References in corpus (26)
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Solvable model for chimera states of coupled oscillators
- Long Time Evolution of Phase Oscillator Systems
- Macroscopic description for networks of spiking neurons
- Partially integrable dynamics of hierarchical populations of coupled oscillators
- Phase oscillators with global sinusoidal coupling evolve by Mobius group action
- Chimeras in networks with purely local coupling
- Low-dimensional dynamics of populations of pulse-coupled oscillators
- Self-Emerging and Turbulent Chimeras in Oscillator Chains
- Dynamics of noisy oscillator populations beyond the Ott-Antonsen ansatz
- Invariant submanifold for series arrays of Josephson junctions
- On the Concept of Dynamical Reduction : The Case of Coupled Oscillators
- Recent Advances in Coupled Oscillator Theory
- Dynamical aspects of mean field plane rotators and the Kuramoto model
- Ott-Antonsen attractiveness for parameter-dependent oscillatory networks
- Collective mode reductions for populations of coupled noisy oscillators
- Interplay of coupling and common noise at the transition to synchrony in oscillator populations
- Chimera patterns in the Kuramoto-Battogtokh model
- Synchronization of coupled active rotators by common noise
- The mathematics of asymptotic stability in the Kuramoto model
- Ott-Antonsen ansatz is the only admissible truncation of a circular cumulant series
- Two Scenarios for the Onset and Suppression of Collective Oscillations in Heterogeneous Populations of Active Rotators
- Interplay of the mechanisms of synchronization by common noise and global coupling for a general class of limit-cycle oscillators
- Relationships between the Distribution of Watanabe-Strogatz Variables and Circular Cumulants for Ensembles of Phase Elements
- Solitary synchronization waves in distributed oscillators populations
- Circular Cumulant Reductions for Macroscopic Dynamics of Kuramoto Ensemble with Multiplicative Intrinsic Noise